Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C4×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #1806 |
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2)(8,10)(9,12)(11,13)(14,15);(4,5,6,7);(2,3)(5,7)(8,9,11,14,12,10,15,13)Polycyclic presentation:
2^7,3|a^2=f,b^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,e^c=eg,h^c=h^278 conjugacy classes — view the full character table.
| maximal subgroup of | #10687094, #10687100, #10687101, … |
| maximal normal subgroup of | #10687094, #10687100, #10687101, … |
| maximal quotient of | #10687871, #10687876, #10687881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2070);